Global Musical Modernisms blog posts (2021 collection)


Featuring posts on music of the following composers from Indonesia, Japan, China, Brazil, Denmark, and the US:

César Guerra-Peixe (Brazil), Trio (1960) (author: Frederico Barros, Federal University of Rio de Janeiro) Guerra-Peixe’s Academic Trio

Hale Smith (US), Three Brevities for Solo Flute (1969) (author: Megan Lyons, University of Connecticut) Hale to the King: “Three Brevities for Solo Flute” by Hale Smith

Per Nørgård (Denmark), Wie Ein Kind (1979-80) (author: Paul David Flood, University of California, Irvine) Per Nørgård’s Two-Tone Infinity Series in “Wie Ein Kind” (1979-80)

Rahayu Supanggah, Paragraph (1991) (author: Jay M. Arms, University of Pittsburgh) Rahayu Supanggah’s “Paragraph” and the Problems of Intercultural Collaborations

Cui Jian (China), Nothing to My Name (released in 1989) & Li Jinhui, Drizzle (1927) (author: Ya-Hui Cheng, University of South Florida) Whose Authorship? Authenticity in Chinese Popular Music under Global Modernism 

Jōji Yuasa (Japan), Cosmos Haptic (1957) (author: Ron Squibbs, University of Connecticut, Storrs) Jōji Yuasa – Cosmos Haptic for piano (1957)

Toshio Hosokawa, Matsukaze (2010) (author: Tomoko Deguchi, Winthrop University) The Appeal of the Foreign in Toshio Hosokawa’s Opera Matsukaze


Global Musical Modernisms is a forum for all forms of music received and appropriated as “modern” in any location around the globe, crossing the boundaries of post/tonality. The focus is primarily but not exclusively on art, avant-garde, experimental, and modernist music, by global (African, Middle Eastern, Central/ South/ Southeast/ East Asian, Latin American, Australasian etc.) composers, minority composers from the West, and composers from the peripheries of Europe and North America.

Authors in each volume serve as peer editors for each other, shaping each post into an accessible piece of writing (with analytical graphs where appropriate) that is a scholarly guide to global musical modernisms and a multi-media teaching resource.

Guerra-Peixe’s Academic Trio

By Frederico Barros


The year was 1960 and Brazilian composer César Guerra-Peixe submitted his Trio, for violin, cello and piano to a contest held by the Brazilian Ministry of Education’s radio station.<1> Click here for the score and recording. On the surface, the piece is illustrative of Guerra-Peixe’s output of the period, but some of its specificities offer interesting points of discussion. From the modal techniques employed and explicit nationalism to the clear structure and tightly-knit thematic work, the Trio shows how Guerra-Peixe positioned himself in the debate about Brazilian music at the time. Some old-school motivic analysis may help us better understand what this means.

The sonata-allegro begins with the first thematic group’s theme 1 (A1), played by violin and cello two octaves apart and clearly related to the Brazilian northeastern region:


Figure 1: Guerra-Peixe – Trio, 1st mov., A1, m. 1-11, violin part


Showing why musical materials are related to a place or human group is a complex endeavor. However, at least in this case, we can let the composer himself speak. In the essay Os Cabocolinhos do Recife,<2> Guerra-Peixe presents examples very similar both to A1 and B2 (figure 5 below).


Figure 2: Examples of Cabocolinhos melodic figures collected by Guerra-Peixe<3>


The origin of the piano accompaniment in A1 (figure 3) is harder to trace, but its rhythmic structure, repeated until m. 10, combined with the range of a major second (with some variation) in the highest voice can be convincingly linked to the “elements of the berimbau” that Guerra-Peixe would later say were present in the Trio.<4>


Figure 3: Guerra-Peixe – Trio, 1st mov., A1, m. 1-2, piano part


The second theme of the first group (A2), by its turn, is based on the cell c from A1—whose rhythm was also heard in the piano left hand in A1 (as shown in fig. 3):


Figure 4: Guerra-Peixe – Trio, 1st mov. Cell c (from A1) and A2 (m. 26-29)


Finally, the piece’s tonal plan goes from D Lydian (A1) to F# Minor (A2), and then to B Dorian on the first theme of the second group (B1). It then reaches A Lydian on the second theme of the second group (B2), the closing theme that brings back the Lydian sound of A1, to which it is clearly related:<5>


Figure 5: Guerra-Peixe – Trio, 1st mov., B2, m. 70-74, piano right hand


From the first group to the second—the foundational polarity of sonata form—the piece descends a minor third, as if going from major to relative minor, but here making a homologous move from D Lydian to B Dorian. Despite B2 being in the dominant region, the modalism present in the Trio takes over the role of the tonal relations in a conventional sonata-allegro. This serves as an entry point into a significant aspect of this piece: Guerra-Peixe stayed rooted in principles from the Western tradition while infusing them with elements of different origins; following sonata procedures by the book, but employing material seen in his time and place as possessing a distinctive Brazilian character.

Some years later, Guerra-Peixe would state that he wrote the Trio in a deliberately academic fashion, hoping it would make it fare better in the contest.<6> Furthermore, the elements indicated above are all fairly common in the Western tradition, usually being considered indicators of good compositional technique, even if somewhat dated. However, these elements tend to be considerably subtler in other works of the composer from the same period, putting the Trio in a somewhat special place in his oeuvre and raising the question of whether we should take all this at face value.

Born in 1914, Guerra-Peixe’s formative years were marked by the rise of the first Modernist generation in Brazil. It was a period of both aesthetic modernization and of coming to terms with the idea of a national art, and throughout the following two decades this two-fold task would converge. In this very same process, the first modernists would oppose those who came before them with charges of eurocentrism and traditionalism, but slowly sliding into being themselves the new established tradition—at least that’s how many of their successors saw them. To add insult to injury, this took place through the participation of many of those modernists in the Getúlio Vargas dictatorial regime.<7> To put it bluntly, during the 1940s younger composers such as Guerra-Peixe tended to see their nationalist-modernist peers as uninteresting, repetitive, and in many cases as actual sellouts.

It was the time when Guerra-Peixe joined the Música Viva group—centered around German composer Hans-Joachim Koellreutter—and got into twelve-tone music, first radically opposing any form of nationalism but then gradually starting to experiment with combining the two trends. His stint with dodecaphony lasted until around 1949, when questions that had been bugging him for a while about who his music could reach and its social utility reached a peak.<8> Guerra-Peixe then plunged both into the Brazilian countryside and in a creative crisis that would eventually lead him to abandon the twelve-tone technique for good in favor of a music that fed heavily from the proto-ethnomusicological researches he had been doing around that time.<9> Having joined the nationalist bandwagon now, he would criticize his new colleagues by turning their own principles against them, with charges of poor knowledge of the country’s traditions and lack of compositional chops.<10>


Figure 6: Guerra-Peixe in 1950


Guerra-Peixe used to show off his knowledge of Brazilian regional cultures by ditching traditional elements of Western music in favor not only of melodic ideas and rhythms—a practice that at the time was common currency for nationalists worldwide—, but also structures, timbres and forms he learned during his countryside excursions. An eloquent example is the first movement of his String Quartet n. 2, from 1958: at first it may seem like an odd sonata-allegro, then one starts wondering if it isn’t a rondo… only to finally, with some luck, find out that the composer employed the form of the cateretê from São Paulo. To make matters even more complicated, we are not dealing with a song form or equivalent, but with something more akin to a sequence of dances or a ritual whose development is mirrored in the piece.<11>

Thus, the meticulous melodic construction and compositional prowess shown in the Trio can be understood as a deliberate act in a very specific sense. Without getting into value judgments, even if Guerra-Peixe may have misevaluated the jury—he received the second prize and the winning piece, by Marlos Nobre, cannot be said to be conservative, after all—, the Trio reveals that he considered them conventional both on aesthetic and technical grounds. It is true that nationalism would bring Guerra-Peixe and the jury together, but he tended to favor (and boast) a more nuanced view of Brazilian music. When we look at the technical side things get even fuzzier, though, as Guerra-Peixe would often also derive procedures from Brazilian folk sources, perhaps risking a relative alienation of an audience more attuned to the Western canon.

That’s much less perceptible in the Trio. We won’t find some alternative form here, but a proper sonata-allegro, and as such the thematic material is orderly presented. While rhythms from one Brazilian state, Bahia, serve as accompaniment to melodic figures from another, Pernambuco, purposefully blurring geographic frontiers, these work in tandem to form a more general, less localized idea of Brazil. Finally, the specific modal elements he resorts to here may sound Brazilian, but below the surface they serve to put very Western structural forces in motion.

This is not to say that elsewhere Guerra-Peixe would always avoid the Western concert music tradition—be it modern or classic-romantic. On the contrary, these are always present in some shape or form, but often transformed: harmony, timbre, developmental procedures, and other aspects of Western musical thinking would be to some extent impacted by the folkloristic investigations he engaged in from the 1950s on. Threading the line that separated his aesthetic demands from the taste of an imagined jury, he ended up exposing some shortcomings of the modernist project he was himself stumbling upon but couldn’t quite fathom at the time, touching on things we are still grappling with today: alternative theories of form, sound, discourse, and drama, amounting to other ways of thinking about music itself which may not even fit in these categories.



<1> Rádio MEC’s II Concurso de Composição Música e Músicos do Brasil.

<2> GUERRA-PEIXE, C. 2007. Estudos de folclore e música popular urbana. Samuel Araújo (org.). Música editada. Belo Horizonte: Editora UFMG.

<3> Ibid.

<4> Liner notes by the composer for the LP Documentos da Música Brasileira, v.17, LP 356-404-203, MEC/Secretaria de Cultura/Funarte. The berimbau is an instrument mostly associated with the capoeira, from Bahia. It plays two pitches—usually close to a major second in Western theory—that are subject to timbral variations through various playing techniques.

<5> FARIA, A. G. 2000. “Guerra-Peixe e a estilização do folclore.” In: Latin American Music Review. vol. 21, no. 2.

<6> See note 4 above.

<7> SCHWARTZMAN, S., H. M. B. BOMENY, V. M. R. COSTA. 2000. Tempos de Capanema. São Paulo, SP: Paz e Terra: Editora FGV; SQUEFF, E., J. M. WISNIK. 2004. Música. São Paulo, Brasil: Editora Brasiliense.

<8> It’s worth mentioning at this point that the Second International Congress of Composers and Music Critics took place in Prague, Czechoslovakia, in 1948 and brought many of the Socialist Realism directives to music. Its influence was strongly felt in Guerra-Peixe’s circle of relations, as Claudio Santoro, one of his colleagues in the Música Viva group, attended the congress as a delegate of the Brazilian Communist Party (PCB).

<9> See ARAÚJO, S. “Introduction” (GUERRA-PEIXE 2007); ARAÚJO, S. 2010. Movimentos musicais: Guerra-Peixe para ouvir, dançar e pensar. Revista USP, (87), 98-109. USP.

<10> For a detailed discussion, see BARROS, F. César Guerra-Peixe: a modernidade em busca de uma tradição. Doctoral dissertation. Departamento de Sociologia. São Paulo, Brazil: Universidade de São Paulo. 2013.

<11> FARIA, A. G. 2007. “Modalismo e Forma na obra de Guerra-Peixe” in: FARIA, A.G.; BARROS, L.O.C.; SERRÃO, R. Guerra-Peixe: um músico brasileiro. Rio de Janeiro: Lumiar.



Frederico Barros is Music History professor at the Federal University of Rio de Janeiro. He has a PhD in Sociology and MPhil and BA in History. Research interests include concert and urban popular musics and arts during the 20th and 21st centuries, modernism, and nationalism.

Hale to the King: “Three Brevities for Solo Flute” by Hale Smith

By Megan Lyons


If one were asked to name a prolific atonal composer, the answers would likely include Arnold Schoenberg, Anton Webern, or Alban Berg; an unlikely answer would be Hale Smith. Growing up, Hale was involved in classical and jazz ensembles, and these musical experiences shaped his eventual approach to composition. A student of Marcel Dick, a colleague and friend of Arnold Schoenberg in the 1920s, Smith combined atonal and serial techniques into his works alongside African-American rhythmic elements. Horace Maxile describes Smith’s oeuvre as reflecting “a sensitive interaction between the worlds of the African-American vernacular and music of the European tradition.” <1>

Three Brevities for Solo Flute, one of Smith’s lesser-known works, was composed in the middle of his career, in 1969. The first movement, dedicated to flutist Nancy Turetzky, opens with two iterations of pitch-class set (027) through a T3 transformation. This trichord is quartal and open to possibilities, a feature Smith utilizes to his advantage in several of his works, such as Evocation. The trichord (027) appears here as a succession of two interval-class (ic) 5’s and is found frequently in jazz-themed works by Smith. <2> The other primary trichord employed by Smith in this movement, (016), appears more sporadically, and is related to (027) though it may seem audibly disconnected. Ic5 is maintained between the two trichords, yet the whole tone found in (027) is contracted into a semitone in (016). Smith utilizes the common ic5 in dyadic moments in order to illicit uncertainty and blur the lines between the two trichords. The dichotomy between these two trichords is further emphasized as (027) is symmetrical and (016) is asymmetrical. Smith plays upon the contrast between these two trichords through alternation and by focusing on their audible difference, the whole tone and semitone. This alternation can be seen in Example 1, which shows the frequency of these two trichords in mm. 1–15. This opposition is played out on a large scale as exactly halfway through the movement, the piece is performed in imperfect retrograde; the symmetry is altered as two measures of unrelated material are inserted in different locations for each half of the piece.


Example 1: Movement I, mm. 1–15


Dedicated to composer Wallingford Riegger, the second movement supposedly features the basic motive of Riegger’s Second Symphony. <3> While the opening movement was characterized by trichords, the second movement emphasizes tetrachords instead. Smith introduces a melodic and rhythmic motive early on in this movement; this (0123) motive is repeated with slight rhythmic variation throughout the movement. The second movement does not end symmetrically as the first did; instead, Smith concludes the movement with an (0235) tetrachord instead. Example 2 shows the opening (0123) motive and the evolved (0235) motive at the conclusion. The interval content of the pitch collection changes from <321000> to <122010>, with the most notable difference being the inclusion of ic5 in (0235). The contrast between the iterations of the motives (0123) and (0235) calls back to the contrast between semitones and whole tones in the first movement, although this time the initial set expands rather than contracts.


Example 2a: Movement II mm. 1–2

Example 2b: Movement II mm. 27–31


For the third and final movement, dedicated to jazz flutist Jerome Richardson, Smith shifts to serialism: complete tone rows are introduced within a traditional ternary form. As seen below in Example 3, four distinct internal trichords and three distinct internal tetrachords can be derived from this row. In retrospect, the compositional choices of the first two movements are found in the row of the third movement. The first movement utilized mainly (027) and (016) trichords while the second movement featured (0123).


Example 3: Movement III Matrix and Subsets


In his analysis of Smith’s Evocations, Maxile notes four row forms that have the same boundary tones, with Smith often linking tone row statements with common tones. <5> The four primary row forms employed in the third movement of Three Brevities are P6, R6, I6, and RI6, clearly linked through pitch-class (pc) 6. P6 is presented first, with pc6 repeated utilizing the rhythmic pattern from the first movement of two sixteenth notes followed by an eighth note. This is unsurprising as Smith is “a motivic kind of composer in that [he] tend[s] to work with a few key motivic ideas” to unify a composition. <6> RI6 follows yet the opening tetrachord is repeated prior to the entire row form being heard. This repeated tetrachord is a member of (0123) and is reminiscent of the second movement tetrachord motive. The beginning of I6 elides with the end of RI6 and once again features the three-note repetition of pc6 from the opening of the movement. Following the sounding of I6, one would expect R6 to appear, yet it does not; Smith’s composition moves to seemingly unrelated material for the B section, recalling motives from the prior movements as well as subsets of the four main tone rows.

One such subset, a hexachord from R6, is repeated four times before continuing on to unique material in the B section. Prior to the return of the A section, the hexachord from R6 is heard again, but this time in retrograde, an allusion to the first movement. This second presentation of the R6 hexachord is the retrograde of the initial presentation. A full iteration of R6 ultimately concludes the movement, completing the four pc6-based row forms.

The retrospective cohesion of Smith’s work is expected given his comments on his own compositional process. In an interview, Smith stated how “one must be able to extract from one’s ideas all of their possibilities. You have this entity that has all sorts of implications.” <7> One such entity is Smith’s near-obsession with ic5, found repeatedly through his compositional choices in this work. The duration of the piece is set at 5 minutes and 15 seconds; the first movement is 50 measures long; the time signature of the second movement is 5/8; and finally, his persistent use of ic5. The connection of ic5 to Smith’s jazz-like pieces is well-known, yet it must be asked: why ic5? Perhaps it allows him to venture into complex musical realms while maintaining a connection to tonality as a perfect fourth/fifth. Perhaps, like Bach, Smith wanted his name to shine in his works; after all, Smith is five letters long. This is only a small sample of Smith’s ability to extract all possibilities from a single entity. Cohesion in Smith’s compositions can be further explained through his idea of a nucleus. “Everything relates from the smallest nucleus through the finished fruit, through the tree itself.” <8> For Three Brevities, the nucleus is without a doubt the row form of the third movement, without which the rest of the piece cannot be understood.

Smith received critical acclaim during his career, having his pieces performed by the New York Philharmonic, the Cleveland Orchestra, and more. Being an active composer in the 1950s and 60s, Smith found himself in the middle of racial discussions: he was often seen as a spokesperson or representative asked to speak on behalf of black artists. Smith stated: “the tendency among many people still is to assume that the black American composer is not on an equal level with his white counterpart.” <9> Smith’s words are reminiscent of Phil Ewell’s groundbreaking work with “Music Theory’s White Racial Frame,” which acknowledges the deficit of Black composers and their work within the Western music canon. <10> Both Smith and Ewell advocate for a reframing of Western music standards to be inclusive rather than exclusive, specifically in regards to the race of composers. In 1971, Smith stated “I have faced the question as to whether or not my work was worthy of appearing on programs of music by the recognized masters of my art.” <11> It is clear, through scratching the surface of just one of Smith’s pieces, that his work is more than worthy of being programmed, analyzed, and included in the Western canon.

The score for Three Brevities for Solo Flute is published by ED Marks Music Company and is available for purchase through Subito Music Corporation. A wonderful performance by Laurel Zucker on flute can be found at the following YouTube links: first movement, second movement, and third movement.




<1> Horace J. Maxile, “Hale Smith’s ‘Evocation’: The Interaction of Cultural Symbols and Serial Composition.” Perspectives of New Music 42, no. 2 (2004): 122, accessed January 30, 2020,

<2> Maxile, 126.

<3> This claim remains unconfirmed, as there are no public recordings of the Second Symphony nor is the score accessible to the public. For more reading on Reigger, see his Britannica Encyclopedia page.

<4>  Hansonia Caldwell and Hale Smith, “A Man of Many Parts,” The Black Perspective in Music 3, no. 1 (1975): 71, accessed January 30, 2020, doi:10.2307/12143081.

<5> Maxile, 125.

<6> Caldwell and Smith, 71.

<7> Caldwell and Smith, 61.

<8> Caldwell and Smith, 65.

<9> Caldwell and Smith, 66.

<10> Phil Ewell’s blog can be found here: His plenary paper at the 2020 SMT national conference can be found here: The MTO article based on the plenary session can be found here:

<11> Hale Smith, “Here I Stand,” in Readings in Black American Music, 1st ed. New York: W.W. Norton, 1971: 286–287.


Megan Lyons is a PhD candidate and graduate teaching assistant in music theory and history at the University of Connecticut. Her research areas include music theory pedagogy, Amy Beach, Joni Mitchell, and post-tonal music. She has an article in Engaging Students: Essays in Music Pedagogy, a forthcoming chapter in Teaching and Learning Difficult Topics in the Music Classroom, and presented at the 2020 annual meeting of the Society for Music Theory.


Per Nørgård’s Two-Tone Infinity Series in “Wie Ein Kind” (1979-80)

By Paul David Flood

When Danish composer Per Nørgård discovered the art of the schizophrenic Swiss painter Adolf Wölfli at an outsider art exhibit in 1979, he was struck by the fractal construction of these paintings and their similarity to his infinity series, a compositional system based on an integer sequence which he claimed to have “discovered” and used in his works throughout his “hierarchical period” of the 1960s and 70s.<1> Nørgård’s study of Wölfli’s tormented life influenced his subsequent compositional output during the early 1980s, sonically framing his existential crisis of how his “ideal” world may be envisioned.<2> At the heart of these works is the notion of conflict between “idyll and catastrophe” within the human experience; the apperception of unhappiness as a necessary part of experiencing happiness.<3> This essay suggests how Nørgård’s crisis manifested in his compositional technique by analyzing his unconventional use of the infinity series in his first work inspired by Wölfli, Wie Ein Kind.


Adolf Wölfli, General view of the island Neveranger, 1911.


Written between 1979 and 1980 on a commission from the Nordiska Körkomittén, Wie Ein Kind frames conflict through its exploration of childlike experiences.<4> The first and third movements, “Wiigen-Lied” and “Trauermarsch mit einem Unglücksfall,” bear motivic similarities and set a nonsense text written by Wölfli. In the first movement, the soloist’s wails and distant cries evoke the image of a street vendor, or a mother calling to her child from a tower. In the third movement, the soloist attempts to conform with the choir but suffers from an embarrassing stutter which keeps them rhythmically misaligned with the choir. The second movement stands in contrast to its bookending movements. Set to Rainer Marie Rilke’s “Frühlings-Lied,” the movement’s harmonic simplicity and playful texture depicts childlike joy and sensual awareness.<5> A later section of this movement employs a reduced form of Nørgård’s infinity series called the two-tone infinity series. As Wie Ein Kind is the first piece written in the Wölfli period of Nørgård’s oeuvre, Nørgård’s reduction of his own technique signifies the manifestation of his crisis in his composition.

The infinity series is a recursive integer sequence built upon the outward projection of intervals, in both directions, beginning from the very first interval of a given row, counted in semitones.<6> This process of intervallic projection can also be used to reduce an infinity series into a two-tone infinity series. I will introduce the infinity series, demonstrate how Nørgård may have reduced his original series into a two-tone infinity series, and discuss the two-tone infinity series within mm. 98-129 of “Frühlings-Lied.” (Note that measure numbers referenced in this essay align to the score which has been made commercially available by Edition Wilhelm Hansen.<10>) These measures contain four units with similar motives in the tenor and alto voices that are constructed by the two-tone infinity series. Each successive unit is varied from its predecessor in texture, pitch collection, and rhythm of the outer voices.


Figure 1: Nørgård, “Frühlings-Lied,” mm. 97-132. Annotated to show beginnings of each unit.


Figure 2 is an infinity row based on the ascent of two semitones from the starting pitch C. This series will be called Inf. C+2, indicating the starting pitch and the respective ordered pitch interval.

Figure 2: The first twelve pitches of Inf. C+2.


The aforementioned process of constructing an infinity series is one in which the ordered pitch intervals from one note to the next are projected to determine the succeeding pitches in a series. Starting from the beginning of the series, the interval of two rising semitones between C to D will determine the following two pitches. The projection of intervals occurs in such a way that every other note is related, as shown by the blue and red arrows in Figure 2. Each interval projects two notes in opposite directions: the first note to be projected will move in relation to the starting pitch, but in the opposite direction of the interval being projected . In other words, the ascent of two semitones between C and D will project a descent of two semitones between C and the Bb after the D. The next note will be projecte d in the same direction as the interval between C and D, but will do so in relation to the D. The ascent of two semitones from C to D will project the same interval between D and the E after Bb. Therefore, in the context of Inf. C+2, the two-semitone ascent from C to D will project itself such that the third note of the series will move two semitones below C, to Bb, and the fourth note of the series will move two semitones above D, to E.  The series then continues with the interval between D and Bb, a descent of four semitones, leading to D and C as the next two pitches in the serie The process continues toward infinity (or at least where the composer decides to stop).<7>

In Wie Ein Kind, Nørgård uses what is called a two-tone infinity series, a reduced form of the infinity series which contains and repeats the same two pitches which began the original infinity series. The repetitive ordering of these two pitches can be identified through the very process of reduction. To convert Inf. C+2 into a two-tone infinity series, we consider the pitches C and D as numerical values 0 and 1. Each successive pitch will be given a value in relation to the starting pitch; Bb is -1, E is 2, Ab is -2, and so on (these values are given based on the number of whole steps above or below C).<8> Each value will then be added to or subtracted from by a multiple of 2 until it becomes either value 0 or 1, as demonstrated by the blue numbers in Figure 3. If the value is above 1, it will be subtracted by a multiple of 2, and if the value is below 0, it will be added to by a multiple of 2.<9>



Figure 3: Process of reduction from Inf. C+2 to 2TInf. C+2.


Given the above examples, provided for technical context, I now turn to the two-tone infinity series that is present in “Frühlings-Lied.” Between measures 98 and 129 are four units based on the two-tone infinity series. Nørgård se ts a larger two-tone infinity series as the basis of these units, including only the consecutively repeating pitches within that series in these units to create what he calls a “pishop” rhythm . A pishop rhythm is the extraction and tying-together of these consecutively repeating pitches from their larger two-tone series.  Repeated notes from the larger series are converted into tied notes in the score, creating the pishop rhythm. Pitches that do not have a repetition before or after themselves are replaced by a rest, as shown in the Figures 4.1 and 4.2  in which the pishop rhythm in the tenor line is isolated to reveal the series 2TInf. E-9.


Figure 4.1: Nørgård, “Frühlings-Lied,” mm. 98-105, tenor.



Figure 4.2: Conversion between tenor pishop rhythm and 2TInf. E-9.


At first glance, there may appear to be discrepancies in this conversion, but these are intentional and unique to each unit. For example, the pishop rhythm containing an eighth note tied to a quarter note is most likely a textural choice, as it is not an indication that three consecutively repeated pitches exist in the two-tone infinity series (this would not be possible based on the process of reduction). In addition, the large distance between the two pitches of the series used in “Frühlings-Lied” means that neither pitch can be identified with values 0 or 1 as in the technical example above. Nørgård’s use of the two-tone infinity series in other works does allow for this identification of numerical value, and even though the series in question does not possess this quality, it is still considered a two-tone infinity series for functional purposes.<11> Nørgård’s use of a two-tone infinity series that is non-derivative is perhaps another manifestation of his crisis and the transition into his Wölfli period.

The introductory unit in mm. 98-105  features two infinity rows in the inner voices while the basses sing in fifths below. The second unit in mm. 106-113 features variation in the outer voices while the content in the inner voices remains the same. Here, the soprano part enters above while the fifths in the bass move by glissandi. The third unit in mm. 114-121 sees multiple variations. First, the soprano line from the previous unit does not return. There is an additional pitch B added to the tenor line. A possible explanation for the addition of this pitch is to align with the first bass’ Bs on m. 115 and m. 116. The most important variation here is disruption of the pishop rhythm at the end of measure 116, where the rhythmic values proceed from quarter note on G, to eighth note on E, to half note on G, rather than three consecutive occurrences of two tied eighth notes. In addition, the alto and tenor parts fall out of alignment for a brief moment in measure 116, where the alto sings an eighth note on beat two but the tenor holds on for a bit longer with a quarter note. The fourth and final unit in mm. 122-129 sees the return of the soprano line with shorter durations of the material from unit two, and the removal of the glissandi from the bass. At the beginning of this unit, the tenor briefly sings a unison D with the alto. This culminating two-tone unit presents slightly obscured inner voice lines, informed by the two-tone infinity series, with motives in the outer voices to provide accompanying texture.

Nørgård’s use of his infinity series in its reduced, non-derivative form harkens as a point of no return, a glimpse into something that once was but which cannot be revived in its original form. Much in the same way, Nørgård’s study of Wölfli challenged his former vision of the ideal world to accommodate outsiders  such as Wölfli. <12> Nørgård did not necessarily intend for this music to be ekphrastic in its content — that is, he did not attempt to illustrate any particular artwork through musical composition. Instead, the Wölfli works originate from Nørgård’s desire to situate himself as a medium through which the “cries and phantasms of a lonely person, afflicted for decades, who suddenly demanded entry into Per Nørgård’s music” could be heard.<13> Wie Ein Kind frames Nørgård’s struggle to abandon his fixation for order in favor of the opportunities presented by chaos: to embrace the outsider, Wölfli, in his shifting ideology and compositional style over the next few years.



<1> Erling Kullberg, “Beyond Infinity: On the infinity series — the DNA of hierarchical music,” in The Music of Per Nørgård: Fourteen Interpretive Essays, ed. Anders Beyer (Brookfield, VT: Ashgate Publishing Co., 1996), 71.

<2> Jean Christensen, “Part I—New Music in Denmark” in New Music of the Nordic Countries, ed. John D. White (Hillsdale, NY: Pendragon Press, 2002), 41.

<3> Erling Kullberg, “Wie Ein Kind for choir a capella,”

<4> Kullberg, “Wie Ein Kind.”

<5> Per Nørgård, Wie Ein Kind (Copenhagen: Edition Wilhelm Hansen, 1996), iii.

<6> For a mathematical explanation of the infinity series, see the entry on the Thue-Morse Sequence in the On-Line Encyclopedia of Integer Sequences:

<7> Jørgen Mortensen, “Construction by the projection of intervals,”

<8> Note that these values are not to be confused with pitch class set theory, in which C is also 0 but D is 2.

<9> Jørgen Mortensen, “An infinity series with only 4 or 2 different variants,”

<10> The score for Wie Ein Kind  is available for purchase at:–Per-N%C3%B8rg%C3%A5rd/.

<11> Kullberg, “Wie Ein Kind.”

<12> Christensen, 42.

<13> Jørgen I. Jensen, “The Great Change: Per Nørgård and Adolf Wölfli” in The Music of Per Nørgård: Fourteen Interpretive Essays, ed. Anders Beyer (Brookfield, VT: Ashgate Publishing Co, 1996), 9.



Paul David Flood is pursuing his Master’s degree in Musicology at the University of California, Irvine. His research focuses on developments of Nordic musical identity and modernism in Denmark. He is currently working on his Master’s thesis, titled “Embracing the Outsider: Framing Conflict in Per Nørgård’s Wölfli Works.” Additional interests also include contemporary music reception, music and philosophy, vocal literature, and the Eurovision Song Contest. He received his B.A. in Music from Westminster Choir College in 2019 and is an active choral singer.


Rahayu Supanggah’s “Paragraph” and the Problems of Intercultural Collaborations

By Jay M. Arms

The 1986 First International Gamelan Festival and Symposium (Expo ’86) was a catalytic event in the globalization of Indonesian gamelan music. Though gamelan ensembles had already been established in different nations and cultural settings around the world—largely because of university ethnomusicology programs—Expo ’86 marked the first formalized event to bring international groups together. The event engendered numerous intercultural collaborations among its participants, especially between composers of experimental music. One of the composers to attend Expo ’86 was Rahayu Supanggah (b. 1949). By the time of Expo ’86, Supanggah had already established himself as a leading composer in Indonesia, served as director of the karawitan (classical gamelan music) department at the conservatory in Surakarta, Central Java, and received his Ph.D. in ethnomusicology from the University of Paris Diderot. <1> Despite Supanggah’s achievements, his music was relatively unknown among the North American and European composers he met at Expo ‘86. <2> The symposium brought together artists of diverse nationalities, inspiring dreams of what American composer Philip Corner imagined as a “quasi-international avant-garde tradition.” <3>

Taking part in that shared dream, Supanggah later participated in a five-week residency in 1991 with New York based composers’ collective and repertory ensemble Gamelan Son of Lion. <4> During his residency, Supanggah regularly rehearsed with composer-members of the group, participated in collective composition projects, and recorded a one-hour free improvisation with Corner. <5> After getting acquainted with Gamelan Son of Lion’s post-Cagean approach to playing and composing for gamelan, Supanggah composed Paragraph (1991), an experimental composition that renders both the enticing and challenging aspects of intercultural collaboration audible. Supanggah explains that this piece “represents a part of my experience working with American gamelan players, just as a paragraph is a portion of a larger essay.” <6>

Intercultural collaborations are challenging by nature. As Supanggah observes, even in situations where all parties meet with the best of intentions and mutual respect, the realities of post-colonial hegemony often lay just beneath the surface: “Up to the present time, the majority of collaborations between artists from different cultures or countries has been … with more orientation towards the West.” <7> In composing Paragraph, Supanggah had to orient his approach toward the abilities of his Gamelan Son of Lion collaborators. Whereas Supanggah is a recognized master of both traditional Central Javanese music and experimental composition, the musicians of Gamelan Son of Lion were relative novices in Karawitan, having focused almost exclusively on idiosyncratic ways of writing and performing gamelan music. This discrepancy became axiomatic to Supanggah’s concept for this piece, writing: “In [my] compositional process, I usually work with musicians who are familiar to me. This, however, is a new experience for both composer and musicians. As a way of sharing with these new musicians, I have used some fundamental Javanese techniques in this piece, as well as some new ones.” <8>

Paragraph consists of five distinct, but contiguous sections (labeled I–V). It uses the two common Central Javanese scales pelog (seven-tone hemitonic) and slendro (five-tone anhemitonic). <9> These scales are notated using a form of cipher notation known as kepatihan that assigns Arabic numerals to different tones: 1, 2, 3, 4, 5, 6, 7, for pelog and 1, 2, 3, 5, 6 for slendro. It is critical to note that although some notes between scales share the same numeral, that does not necessarily mean they are of the same pitch. <10> Though traditionally these scales are not mixed, Gamelan Son of Lion composers experimented with combining these scales to create new ones beginning in the 1970s. In Paragraph, Supanggah does not combine the scales, but instead, juxtaposes them in such a way that each retains its own identity while sometimes sounding simultaneously.

The opening of the piece (Part I) uses the pelog scale and features a simple repeating cycle. The instruments used here are mostly keyed metallophones that each play one octave of the scale. From the highest octave to the lowest, these metallophones are called peking, (labeled SP in Example 1), saron (SB), demung (DM), and slenthem (SL). These instruments join the piece one at a time in descending order from highest to lowest in a gradual process of accumulation. Such processes are fairly typical of Gamelan Son of Lion compositions, and Supanggah’s adoption of it here may be a nod to the group for which the piece is composed. In Example 1, all parts are notated together despite entering one at a time to save space in the score.


Example 1. First phrase of Paragraph


Once all of these melodic instruments are present, the large gongs begin to articulate a colotomic structure reminiscent of a karawitan composition. After a few repetitions of this complete texture, a brief transition played in unison leads to Part II, in a tempo twice as fast as that of Part I and using a different pathet (mode) of the pelog scale that ushers in a new character. This lively, jubilant section expresses a feeling of excitement in terms of both tempo and tonality, alternately cadencing on pelog 6 and 7. The mood seems to suggest the sheer joy of playing together and the sense of excitement swells before coming to an abrupt halt.

Part III follows immediately with more contemplative, pensive mood. It consists of an improvisation played on gender (multi-octave metallophone), suling (end-blown bamboo flute), and Chinese erhu (bowed spiked fiddle). This improvisation is modeled on the Central Javanese practice of pathetan, short pieces in free rhythm in which three or four instruments weave together their semi-improvised melodies that diverge from and converge to goal tones. <11> The use of pathetan, a subtler genre of Central Javanese music, suggests more than a mere aesthetic contrast to Part II. Whereas the composer-musicians of gamelan Son of Lion have a proficiency in playing the basic instruments of a gamelan, pathetan requires a deeper knowledge of Javanese music theory than most of the musicians have had. By including a pathetan in this composition, Supanggah brings into focus some of the limitations of collaboration itself: the abilities of all collaborators shape the potential of the results. For Paragraph, the pathetan was played by Supanggah, his colleague composer I Wayan Sadra, and ethnomusicologist Barbara Benary, excluding the musicians who lacked such skills.

Part IV begins immediately as Part III comes to close. The ensemble gradually re-enters the piece through another accumulating process that layers different ostinati in the slendro scale. Once all of the ostinati are cycling, the texture devolves into a free improvisation involving all manner of instruments. <12> This section taps into the egalitarian idealism often associated with free improvisation and which some members of Gamelan Son of Lion projected onto gamelan ensembles in general. <13> This improvisation builds in intensity, and then begins to simplify and become quieter, leading to the fifth and final section.


Example 2. Layered Ostinati in Part IV


The parable of collaboration culminates in Part V. This section brings together the themes that preceded it in stark juxtaposition. Some of the instruments return to the pelog material of Part II, while other instruments introduce a new melody in slendro, creating haunting effect. The jubilant melodies from Part II emerge first, insistently silencing the collective improvisation of Part IV and asserting one vision of unification out of the chaos. But that vision is subverted shortly thereafter by the slendro material that articulates a contrasting, even incompatible vision of its own. The mixing of these scales is highly unusual in a traditional setting, and the dissonances created through this juxtaposition are recognizable even to the uninitiated listener. We learn at the end that no true synthesis has occurred in the course of the collaboration. Each theme remains effectively unchanged by the encounter and unobservant of the other cohabitating the musical space. The piece is suddenly brought to an end by a stroke of a gong, with no resolution of the dissonant mash-up.

Throughout the piece Supanggah guides the listener through a journey. Each section can be understood to represent a certain aspect of the collaborative process: methodical discovery; excitement; realization of limitations, exploration; and finally, Paragraph presents a skeptical outlook on the nature of intercultural collaborations. It is a well-crafted composition that techniques of New York experimentalism and Central Javanese karawitan alternate. But Paragraph does not simply celebrate its syncretism or reassure the listener of an unproblematic multiculturalism. Supanggah encourages us to consider the kinds of compromises that must be made in such collaborations and who is expected to make those compromises. He writes, “It is not uncommon, due to a high level of enthusiasm and willingness to make sacrifices, for a participant to be ‘willing’ to throw off his own identity, and subsequently melt and become or make something new … based on inadequate (mutual) understanding.” <14> In some ways Paragraph can be heard as such a capitulation to the limited abilities of the group. But the ending juxtapositions suggest a more complicated interpretation in which the composer refused to compromise his own artistic sensibilities and instead utilized the imbalanced experiences of the performers to formulate a deeper meaning for the composition.





<1> See Vincent McDermott, “Gamelans and New Music,” The Musical Quarterly 72, No. 1 (1986): 16–27 for more background on Supanggah.

<2> Today Supanggah is internationally recognized for his own compositions, scholarly writings, and for his numerous high-profile intercultural collaborations such as Peter Brook’s Mahabarata (1994), Ong Keng Sen’s Lear (1995), and Robert Wilson’s I La Galigo (2004), and Garin Nugroho’s Opera Jawa (2006) and Setan Jawa (2017).

<3> Philip Corner quoted in Jody Diamond, “Philip Corner: You Can Only Be Who You Are,” Balungan 2, No. 3 (1986): 23.

<4> The residencies were organized by composer Jody Diamond as part of the Festival of Indonesia, a series of NEA sponsored events that took place in different locations around the United States. The residencies produced several compositions and collaborations between American and Indonesian composers that are documented and recorded in Jody Diamond, “Interaction: New Music for Gamelan,” Leonardo Music Journal 2, No. 1 (1992): 97–98.

<5> Rahayu Supanggah and Philip Corner, “Together in New York,” Setola Di Maiale (2015): SM2760.

<6> Rahayu Supanggah, Program notes for Paragraph, Concert program for Experimental Composers From Indonesia: New Music by Rahayu Supanggah and I Wayan Sadra November 20, 1991. Accessed August 8, 2020,

<7> Rahayu Supanggah, “A Story of Arts Collaboration,” Proceedings of the First Asia-Pacific Arts Forum (2000): 399.

<8> Rahayu Supanggah, Program Notes for Paragraph.

<9> The score for Paragraph is published by the American Gamelan Institute. Accessed August 8, 2020,

<10> In fact, the tuning of each gamelan is unique, and compositions generally sound different when transferred from one gamelan to another. Gamelan Son of Lion’s scales share two common tones between the scales known as tumbuk. Pitch 6 is the same between slendro and pelog, and slendro 5 is the same pitch as pelog 4.

<11> See Benjamin Brinner, “At The Border of Sound and Silence: The Use and Function of Pathetan in Javanese Gamelan,” Asian Music 21, No. 1 (1989/90): 1–34.

<12> In the recording and premier performance, this improvisation involved the full gamelan, clarinet, electric bass, erhu, piano, suling, trombone, and violin, though any other instruments would also be accepted.

<13> For example, See Daniel Goode, “How Can the Orchestra be More Like the Gamelan?,” New Music Box, accessed October 2, 2020,

<14> Rahayu Supanggah, “A Story of Arts Collaboration,” 403.




Jay M. Arms is a lecturer of ethnomusicology at the University of Pittsburgh where he teaches the West Javanese gamelan ensemble. His research focuses on the globalization of gamelan music and its intersections with American experimental music and ethnomusicology. He is the co-editor of the journal Balungan that regularly publishes articles and scores related to gamelan and its related arts.